Proportional Volume Sampling and Approximation Algorithms for A-Optimal Design
Bibliographic record
Abstract
We study optimal design problems in which the goal is to choose a set of linear measurements to obtain the most accurate estimate of an unknown vector. We study the [Formula: see text]-optimal design variant where the objective is to minimize the average variance of the error in the maximum likelihood estimate of the vector being measured. We introduce the proportional volume sampling algorithm to obtain nearly optimal bounds in the asymptotic regime when the number [Formula: see text] of measurements made is significantly larger than the dimension [Formula: see text] and obtain the first approximation algorithms whose approximation factor does not degrade with the number of possible measurements when [Formula: see text] is small. The algorithm also gives approximation guarantees for other optimal design objectives such as [Formula: see text]-optimality and the generalized ratio objective, matching or improving the previously best-known results. We further show that bounds similar to ours cannot be obtained for [Formula: see text]-optimal design and that [Formula: see text]-optimal design is NP-hard to approximate within a fixed constant when [Formula: see text].
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.029 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".